Chapter 7.5, Problem 12OE

a)

To determine

To determine whether the parabola opens upward or downward.

Answer to Problem 12OE

Parabola opens upward

.

Explanation of Solution

Given information :

Given equation $y-4=2{\left(x-5\right)}^2$

We know that the graph of the equation $y-k=a{\left(x-h\right)}^2$ opens upwards when $a>0$ and downwards when $a<0$ .

The coordinates of the vertex is given by $\left(h,k\right)$

Axis of symmetry is given by the value of $h$

Now we compare the given equation with the standard equation, we get,

Here the value of $a=2,\left(a>0\right)$ hence the graph of parabola opens upwards.

b)

To determine

The coordinates of the vertex.

Answer to Problem 12OE

Coordinates of the vertex is (5, 4)

.

Explanation of Solution

Given information :

Given equation $y-4=2{\left(x-5\right)}^2$

We know that the graph of the equation $y-k=a{\left(x-h\right)}^2$ opens upwards when $a>0$ and downwards when $a<0$ .

The coordinates of the vertex is given by $\left(h,k\right)$

Axis of symmetry is given by the value of $h$

Now we compare the given equation with the standard equation, we get,

$k=4$

And $h=5$

Therefore the coordinates of the vertex is (5, 4)

c)

To determine

The equation of the axis of symmetry.

Answer to Problem 12OE

Axis of symmetry is $x=5$

.

Explanation of Solution

Given information :

Given equation $y-4=2{\left(x-5\right)}^2$

We know that the graph of the equation $y-k=a{\left(x-h\right)}^2$ opens upwards when $a>0$ and downwards when $a<0$ .

The coordinates of the vertex is given by $\left(h,k\right)$

Axis of symmetry is given by the value of $h$

Now we compare the given equation with the standard equation, we get,

$h=5$

Therefore the coordinates of the vertex is (5, 4)

Axis of symmetry is $x=5$